Dog on a hill, one overseeing museum (7)
I believe the answer is:
curator
'one overseeing museum' is the definition.
'dog on a hill' is the wordplay.
'dog' becomes 'cur' (cur is a kind of dog).
'on' is a charade indicator (letters next to each other).
'hill' becomes 'tor' (tor is a kind of hill).
'cur'+'a'+'tor'='CURATOR'
(Other definitions for curator that I've seen before include "Artistic director" , "Museum officer" , "Museum's administrative head" , "Museum official" , "Guardian" .)